NeurIPS 2026 Papers

Sequence prediction methods for dynamical systems with long memory, i.e. marginally stable systems, typically achieve regret that grows polynomially with the hidden dimension of the underlying generative model. Universal Sequence Preconditioning (USP) \cite{marsdenuniversal} is a method that compresses any sequence which comes from a linear dynamical system into a ``preconditioned'' sequence which requires exponentially shorter memory for accurate prediction. However, the preconditioned sequence yields exponentially larger diameters and gradients, hindering USP from unlocking optimal regret bounds. Inspired by the minimum description length principle, we show that the Vovk-Azoury-Warmuth (VAW) algorithm is naturally matched to the USP regime. Indeed, it takes advantage of the memory compression while remaining robust to the exponential explosion of the diameter. We prove that combining USP with VAW achieves astoundingly strong results: for any marginally-stable linear dynamical system, this algorithm achieves polylogarithmic regret $O\left( \log^3 T \right)$ even in the presence of asymmetric hidden transition matrices. Finally, we extend the applicability of USP beyond bounded-spectrum systems by providing new complex-analytic bounds on Chebyshev polynomials, allowing for systems with constant complex arguments.

We study dynamic pricing where a seller repeatedly interacts with a strategic, non-myopic buyer who has a fixed private valuation and discounts future utility. Prior work focused exclusively on posted-price mechanisms, where the seller gives a take-it-or-leave-it offer. For our first result, we show that menu mechanisms consisting of allocation-payment achieve $O(T_\gamma \log T_\gamma)$ regret, where $T_\gamma$ is the buyer's effective discounted time horizon. We also establish a $\Omega(T_\gamma)$ lower bound, demonstrating the bound is tight up to $\log$ factors. Considering the geometric discounting buyer with a constant discount factor, our bound is $O(1)$, while prior bounds using posted-price mechanisms incur an unavoidable $\Omega(\log\log T)$ factor in regret. Our second contribution is more conceptual in nature. The problem of dynamic pricing sits at the intersection of two paradigms: learning with strategic agents in computer science / machine learning and revelation-principle-based mechanism design in economics, yet their relationship has remained unclear. We establish a fundamental equivalence: indirect learning-based mechanisms and direct revelation mechanisms achieve identical optimal regret. The adaptive, data-driven algorithms of online learning and explicit type elicitation are two languages towards solving the same problem.

This position paper argues that the sequential supervised fine-tuning followed by reinforcement learning (SFT-then-RL) pipeline---the de facto paradigm for large language model (LLM) post-training---has a fundamental property that cannot be fixed by hyperparameter tuning: SFT and RL optimize over nearly orthogonal parameter subspaces, so RL inevitably degrades the capabilities acquired during the preceding SFT phase. Under the PL condition, we show that this degradation scales linearly with the number of model parameters. Although the KL penalty can constrain distributional shift, it cannot correct the underlying gradient misalignment between the two objectives. Experiments on Qwen3-0.6B across four tasks confirm the theoretical predictions: on MATH-500, Alpaca, HH-RLHF, and SST-2, the SFT loss increases after the RL phase. We identify the underlying mechanism as persistent near-orthogonality between the gradients of the two objectives ( $\cos(g_\mathrm{SFT}, g_\mathrm{RL}) \approx 0$), paired with opposing curvature dynamics: SFT flattens the loss landscape while RL re-sharpens it. Based on our analysis, we propose three promising research directions: (1) joint optimization of the two objectives with gradient surgery to resolve conflicting updates; (2) landscape-aware scheduling that terminates RL training precisely at the theoretically optimal point; and (3) characterizing the model scale threshold above which SFT becomes unnecessary.

We present the PokéAgent Challenge, a large-scale benchmark for decision-making research built on Pokémon's multi-agent battle system and expansive role-playing game (RPG) environment. Partial observability, game-theoretic reasoning, and long-horizon planning remain open problems for frontier AI, yet few benchmarks stress all three simultaneously under realistic conditions. PokéAgent targets these limitations at scale through two complementary tracks: our Battling Track, which calls for strategic reasoning and generalization under partial observability in competitive Pokémon battles, and our Speedrunning Track, which requires long-horizon planning and sequential decision-making in the Pokémon RPG. Our Battling Track supplies a dataset of 20M+ battle trajectories alongside a suite of heuristic, RL, and LLM-based baselines capable of high-level competitive play. Our Speedrunning Track provides the first standardized evaluation framework for RPG speedrunning, including an open-source multi-agent orchestration system that enables modular, reproducible comparisons of harness-based LLM approaches. Our NeurIPS 2025 competition validates both the quality of our resources and the research community's interest in Pokémon, with more than 100 teams competing across both tracks and winning solutions detailed in our paper. Participant submissions and our own baselines reveal considerable gaps between generalist (LLM), specialist (RL), and elite human performance. Analysis against the BenchPress evaluation matrix shows that Pokémon battling is nearly orthogonal to standard LLM benchmarks, measuring capabilities not captured by existing evaluation suites and positioning Pokémon as an unsolved benchmark that can drive RL and LLM research forward. We transition from the NeurIPS 2025 competition to a living benchmark by releasing a live leaderboard for Battling and self-contained evaluation for Speedrunning at https://pokeagentchallenge.com.

Fairness impossibility results often look like distinct scalar incompatibility statements. We show that several share one RKHS geometry: fairness criteria are linear constraints on conditional mean embeddings, and unequal base rates make the law of total expectation overdetermine those constraints. This view yields four results. The Kleinberg--Mullainathan--Raghavan dichotomy needs only group-conditional unbiasedness, not full calibration. The \emph{Pok\'emon theorem} shows that a distinct group pair satisfying any finite collection of linear mean-fairness criteria leaves a residual violation witnessed by the MMD, decaying at the Kolmogorov $m$-width rate under spectral regularity. The same tools prove an impossibility for fair feature learning: parity and class-conditional separation in representation space force class collapse under unequal base rates. The approximate relaxations yield signal and error frontiers, allowing a trade-off between real-world estimators and fairness goals. Experiments on standard fairness benchmarks are consistent with our bounds.

Self-supervised learning (SSL) pretrained models have become a dominant paradigm for visual representation learning, but they are vulnerable to backdoor attacks. Existing defenses struggle to defend against such attacks in a fully black-box setting because they often require access to labels, attack patterns, or training data. To tackle this issue, we propose a new attack-agnostic, model-agnostic, and modality-agnostic black-box test-time defense paradigm, called \emph{Platonic Representation Defense}. It is inspired by the Platonic Representation Hypothesis, which suggests that large-scale independently trained encoders converge toward compatible projections of the same underlying reality. We formalize this idea as a conditional energy function defined over source representations and a set of reference representations. The energy function is trained for detection through noise-contrastive estimation and for representation purification through denoising score matching. Theoretically, the energy gap between matched and mismatched samples is lower bounded by the mutual information between source and reference representations. We demonstrate the effectiveness of our method on multiple self-supervised encoders and more than 10 attacks. The method can perform both representation detection and purification, and achieves substantial performance gains across multiple attacks. Code can be found in the appendix.

The mechanisms behind LLMs' broad generalization beyond training examples are poorly understood. Emergent misalignment (EM) offers a striking case study: finetuning on narrow tasks induce broad misalignment to semantically-unrelated test domains. In this work, we propose the Piggyback Hypothesis: the chat-template prefix, shared across all user queries, can piggyback the finetuned behavior onto out-of-domain queries. We validate this hypothesis by showing that subtle perturbations to the prefix, or simply patching the prefix representations with those from the unfinetuned model, can restore alignment without changing the user query. Building on this finding, we propose Token-Regularized Finetuning (TReFT), which directly regularizes prefix representations during training to mitigate piggybacking. Across Llama-3.1, Qwen-2.5, and GPT-OSS models and multiple EM-inducing datasets, TReFT reduces EM while preserving in-domain learning. On Llama-3.1-8B finetuned on the legal domain, TReFT achieves 33.5\% more EM reduction than data interleaving with a retain set of aligned examples. We further show that TReFT extends to other narrow-finetuning settings, including abstention, tool use, and refusal (off-topic generalization is reduced by 54.3\% on average), which further supports the Piggyback Hypothesis. Broadly, our work highlights that LLMs may learn and generalize in unintended ways and suggests a path toward more controllable finetuning. It also calls for further study of how shared input features can piggyback model behavior across domains.

RLVR reliably improves reasoning, yet it appears to update only a tiny fraction of weights. We resolve this paradox by revealing a persistent, model-conditioned optimization bias: independent runs concentrate updates in similar parameter regions, invariant to dataset or RL recipe, while finite-precision storage (e.g., bf16) obscures widespread micro-updates as a visual sparsity artifact. To characterize this unique bias, we show that RLVR preferentially learns along off-principal directions via a cascaded Three-Gate mechanism: updates are first bounded by a empirical KL constraint (Gate I), then steered by the model’s anisotropic geometry(Gate II) toward spectrum-preserving off-principal subspaces, and finally filtered by finite precision (Gate III), effectively masking minor updates. Empirically, we validate the off-principal dynamics: RLVR exhibits minimal spectral drift, reduced principal-subspace rotation, and strong off-principal alignment that set RLVR strikingly apart from SFT. Together, our results provide the first parameter-space account of RLVR and uncover consistent regularities in weight evolution, advancing a more white-box understanding of RLVR. Moreover, we show that RLVR follows an optimization regime distinct from SFT, showing directly that transferring SFT-era PEFT can be flawed and motivating geometry-aware, RLVR-native methods.

Sortition is the practice of delegating public decision-making to randomly selected panels. Recently, it has gained momentum worldwide through its use in citizens' assemblies, sparking growing interest within the computer science community. One key appeal of sortition is that random panels tend to be more _representative_ of the population than elected committees or parliaments. Our main conceptual contribution is a novel definition of representative panels, based on the Wasserstein distance from statistical learning theory. Using this definition, we develop a framework for analyzing the _panel complexity_ problem—determining the required panel size to ensure desirable properties. We focus on three key desiderata: (1) that efficiency at the panel level extends to the whole population, measured by social welfare; (2) that fairness guarantees for the panel translate to fairness for the population, captured by the core; and (3) that the probability of an outlier panel, for which the decision significantly deviates from the optimal one, remains low. We establish near-tight panel complexity guarantees for these desiderata across two fundamental social choice settings: facility location and participatory budgeting.

Hypernetwork-based methods such as Doc-to-LoRA internalize a document into an LLM's weights in a single forward pass, but they fail systematically when the document contradicts pretraining knowledge: accuracy drops to 46.4% on the deepest conflicts. We show that this failure is primarily a magnitude problem rather than a representational one. The generated adapter reaches the relevant layers, but its adapter margin is not calibrated to the strength of the contradicted prior; as the pretrained margin grows, deep conflicts lose the override competition. This account predicts that failure should track prior strength. Sorting 194 conflicts by the base model's log-probability on the contradicted fact, baseline accuracy falls from 68% on weak-prior questions to 16% on strong-prior questions, a 52 percentage-point gap. We propose two training-free corrections. Selective Layer Boosting (SLB) scales the adapter at its highest-activity layers, and Conflict-Aware Internalization (CA) applies stronger boosting only when the base model appears confident. Together they raise deep-conflict accuracy from 46.4% to 71.0% on Gemma-2B and from 53.6% to 72.5% on Mistral-7B, while preserving novel-knowledge recall at 97.1%. They outperform vanilla retrieval-augmented generation on Gemma medium conflicts by 18 percentage points, though explicit conflict-aware prompts remain stronger when the user already knows a conflict exists. We release KID-Bench, a 489-question benchmark that separates novel recall, cross-knowledge combination, and prior-graded conflicts.

Initialization determines the optimization ``fate'' of a model, going far beyond just setting the scale of its weights. It establishes a fundamental initial geometry over the data, permanently dictating which examples are considered close, which directions are easy to change, and which representations gradient descent will naturally refine first. Because this starting point dictates the model's future trajectory, we ask: can this initial geometry be explicitly chosen by referencing a completely different architecture? To achieve this, we introduce representational similarity as an optimization prior. This is an initialization-only procedure that aligns a target network to the representational geometry of a randomly initialized guide network before any downstream training occurs. Crucially, the guide network transfers no learned knowledge: it is frozen, never sees labels. We demonstrate that this cross-architecture transfer of fate works in two key domains: instilling the optimization benefits of depth into shallow targets by aligning them to deeper, randomly initialized guides, and transferring representational granularity by using fine-resolution guides to shape the initialization geometry of networks built with coarser representations. Ultimately, this establishes that a model's architectural destiny can be decoupled from its physical structure and explicitly programmed at initialization.

The feed-forward propagation through neural networks is crucial for training and inference. To trade off efficiency and accuracy, it has been proposed to consider intermediate outputs of hidden states as data-dependent regularization during training and, ultimately, as early-exits during inference. In this work, we analyze the joint optimization of loss functions computed for the output layer and intermediate layers using optimal control theory. We prove that ResNets trained in this joint fashion exhibit the so-called turnpike phenomenon, this implies that the number of layers required to reach a prescribed loss level is bounded from above independently of the overall network depth. This induces a similarity property across the internal representations of early-exiting networks of varying depths. We connect the turnpike to the overthinking phenomenon, and provide theoretical insights of the success of early-exit criteria derived from softmax probabilities, specifically entropy and max-probability. In a range of experiments, we demonstrate the existence and effect of turnpikes and the resulting similarity in the early-exit performance for ResNets of varying depths.

We present the Multi-Block DC (BDC) class, a rich class of structured nonconvex functions that admit a DC (``difference-of-convex'') decomposition across parameter blocks. This multi-block class not only subsumes the usual DC programming, but also turns out to be provably more powerful. Specifically, we demonstrate how standard models (e.g., polynomials and tensor factorization) must have DC decompositions of exponential size, while their BDC formulation is polynomial. This separation in complexity also underscores another key aspect: unlike DC formulations, obtaining BDC formulations for problems is vastly easier and constructive. We illustrate this aspect by presenting explicit BDC formulations for modern tasks such as deep ReLU networks, a result with no known equivalent in the DC class. Moreover, we complement the theory by developing algorithms with non-asymptotic convergence theory, including both batch and stochastic settings, and demonstrate the broad applicability of our method through several applications.

Evaluating enterprise LLMs on file-grounded Question Answering (QA) requires large, labeled corpora of realistic enterprise PDFs, yet real documents are sensitive, scarce, and impossible to annotate at scale. Existing synthetic approaches produce visually crude renders, annotate ground truth post-hoc (introducing hallucination risk), or are non-reproducible one-off scripts with no diversity control. We present SynthDocQA, an Intermediate Representation(IR)-driven pipeline that co-generates photorealistic multi-page enterprise PDFs and provenance-grounded evaluation pairs in a single pass. A compact Document Generation IR encodes topic, content schedule, and perturbation profile before rendering begins. Templates are retrieved per page via Contrastive Language-Image Pretraining (CLIP) embedding-based cross-modal search over a 10,000-layout library; a 15-stage physical degradation pipeline models five scan quality tiers from pristine to poor. Every QA assertion is derived analytically from the same structured artifact that populated the page, making hallucination structurally impossible, and a hierarchical fork-based Random Number Generator (RNG) guarantees exact reproducibility from a single integer seed. A reference 100-document corpus spans 50 enterprise domains, 4,374 pages, 16,589 QA pairs, and 21,402 assertions at zero annotation cost.

Reinforcement learning (RL) has gained growing attention in large language model (LLM) post-training, yet RL training remains fragile and can suffer from instability or collapse. One vital cause is \textit{training-inference mismatch}: % different from traditional RL, the engineering design of LLM adopts separate inference and training engines for generation efficiency and training precision, which in practice exhibits inconsistent probabilities for the same trajectories on training and inference sides, even with synchronized model parameters. This naturally induces a special type of off-policyness ever existing and poisoning the training. Prior works have made various efforts in addressing the off-policyness to stabilize the training policies under the mismatch. In this paper, we point out the \textit{object misalignment} neglected by existing works that an effective update to the policy in the training engine not necessarily ensures the improvement of the inference policy, i.e., the one used in deployment. To this end, we propose a new policy optimization objective for LLM RL, named \textbf{Monotonic Inference Policy Improvement (MIPI)}. Following this principle, we introduce {Monotonic Inference Policy Update (MIPU)}, a two-step LLM RL framework that constructs sampler-referenced candidate updates and selectively accepts synchronized candidates using an inference-side gap proxy. Experiments under high mismatch show that {MIPU} improves average reasoning performance and training stability.

We characterize the minimax rate of estimating the second-order calibration error for binary classification, which quantifies whether a higher-order predictor's epistemic-uncertainty estimate matches the conditional variance of the label probability on its level sets. Our key observation is that the sech perturbation kernel, previously used only to enforce smoothness of calibration functions, in fact makes them \emph{analytic} in a strip of half-width $h\pi/2$. Polynomial regression then estimates the calibration error at rate $\tilde{O}(1/\sqrt{n})$, with explicit constants, a qualitative improvement over the $O(n^{-1/4})$ rate achievable by bucketing or kernel smoothing. A matching $\Omega(1/\sqrt{n})$ lower bound establishes minimax optimality up to logarithmic factors. As a corollary, we give the first finite-sample guarantee for second-order Platt scaling, yielding a post-hoc procedure that recalibrates both the mean prediction and the epistemic-variance estimate of any higher-order predictor. Along the way, we provide a bucket-free definition of second-order calibration and relate it quantitatively to the bucketed formulation of Ahdritz et al. [2025]. Our experiments confirm the predicted rate and the quality of the recalibrated uncertainties.

Kotłowski et al. (NeurIPS 2017) posed as a central open problem the design of efficient online isotonic regression algorithms beyond totally ordered domains. We resolve this for the product order $[m]\times[m]$, the canonical two-dimensional case, by determining the minimax regret up to constant factors: $$ R_T^* = \Theta\left(\min\left\\{T,\ \inf_{K \in \mathbb{N}_+}\left[\log\Omega([m]^2, K+1) + \frac{T}{K^2}\right]\right\\}\right), $$ where $\Omega(\mathcal{P}, K+1)$ is the order polynomial counting monotone maps from $\mathcal{P}$ to $[K+1]$. This unified formula reveals a three-phase scaling law: $\Theta(T)$ for $T \lesssim m$, $\Theta(m^{2/3} T^{1/3})$ for $m \lesssim T \lesssim m^4$, and $\Theta(m^2 \log(T/m^4))$ for $T \gg m^4$. We further construct polynomial-time algorithms achieving this rate in every regime, including a horizon-free variant requiring no advance knowledge of $T$.

Existing 3D Gaussian Splatting (3DGS) segmentation methods produce accurate rendered masks yet often fail to select a complete set of object Gaussians: removing the predicted Gaussians leaves the rendered depth in the target region nearly unchanged. We trace this gap to the contribution-weighted supervision path of rendering-based feature learning. Because Gaussian geometry and opacity are pre-optimized for RGB reconstruction, rendered-feature losses deliver strong gradients only to high-contribution Gaussians, leaving other Gaussians in the same object region weakly supervised and ultimately unselected. We propose VODA, a plug-and-play supervision objective that addresses this bias. After RGB optimization, Gaussians of the same object portion concentrate at similar depths along the camera ray. A depth-aware rasterizer exploits this property, grouping per-pixel contributing Gaussians into depth-coherent clusters and selecting the cluster that best explains each object pixel. The rendered feature of the selected cluster is then applied as a target directly to every Gaussian within it, bypassing the contribution-weighted gradient path. A complementary pixel-level loss further sharpens boundaries between adjacent objects. To evaluate volumetric completeness, we introduce Removal-3D and the Removal Depth Error (RDE), which measure whether removing the predicted Gaussians induces the expected depth change in 3D. Across four rendering-based baselines, VODA consistently improves volumetric segmentation on Removal-3D while maintaining or improving standard performance on LERF and ScanNet.

Neural circuits are infamously more robust than their deep network counterparts. Biology often explains this through degeneracy, where structurally distinct configurations support the same function. Deep learning studies a parallel phenomenon through mode connectivity, which links same-objective networks by low-loss curves, sheets, or volumes. Yet real biological systems undergo continual structural change, a more flexible form of degeneracy in which specialized circuits gradually adapt toward new competencies through localized changes while preserving existing function. The analogous question in deep learning is harder than ordinary mode connectivity, asking whether many independently initialized models trained on distinct tasks can be connected by a high-dimensional region of competent multi-task solutions. We introduce Nimbus, which learns a high-dimensional Bézier manifold connecting N specialists, going beyond the one-dimensional paths and two-dimensional sheets of prior mode connectivity work. A naive parameterization would scale combinatorially with N, but Nimbus requires only a small number of learned correction tensors shared per interaction order, showing that the connecting manifold has surprisingly low complexity yet supports multi-task competencies. The resulting manifold from Nimbus forms a navigable "Marauder's Map" connecting independently trained specialists through a shared geometry of competent solutions. Across vision (CIFAR-100) and language modeling (five disjoint text domains), Nimbus produces manifolds that are both functionally and locally weight-flat. Ensembles sampled from them degrade more gracefully than baselines under input and weight perturbations, with the largest gains in negative log-likelihood and expected calibration error. Beyond its empirical behavior, Nimbus supplies a deep learning interpretation of flexible degeneracy, recasting the connectivity between specialized circuits from a low-dimensional path between distant solutions into a high-dimensional volume of nearby ones.